Local C2-smooth spline quasi-interpolation methods Barrera Rosillo, Domingo Eddargani, S. Ibáñez, M.J. Remogna, S. Quasi-interpolation Bernstein basis BB-coefficients In this paper we construct new univariate local C2 quasi-interpolating splines having specific polynomial reproduction properties. The splines are directly determined by setting their Bernstein-Bézier coefficients to appropriate combinations of the given data values. In certain cases we obtain a family of quasi-interpolating operators satisfying the required conditions, so we fix some extra properties (interpolation of the vertices, extra locality, extra polynomial reproduction) in order to compute unique approximants. We also provide numerical results confirming the theoretical ones 2024-11-19T10:51:49Z 2024-11-19T10:51:49Z 2024-11-05 journal article Barrera Rosillo, D. et. al. Applied Mathematics Letters 160 (2025) 109346. [https://doi.org/10.1016/j.aml.2024.109346] https://hdl.handle.net/10481/97079 10.1016/j.aml.2024.109346 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Elsevier